| #### Chapter 4 |

| #### #### We are told that number is Quantity in the primary sense, number together with all continuous magnitude, space and time: these are the standards to which all else that is considered as Quantity is referred, including motion which is Quantity because its time is quantitative- though perhaps, conversely, the time takes its continuity from the motion. #### If it is maintained that the continuous is a Quantity by the fact of its continuity, then the discrete will not be a Quantity. If, on the contrary, the continuous possesses Quantity as an accident, what is there common to both continuous and discrete to make them quantities? #### Suppose we concede that numbers are quantities: we are merely allowing them the name of quantity; the principle which gives them this name remains obscure. #### On the other hand, line and surface and body are not called quantities; they are called magnitudes: they become known as quantities only when they are rated by number-two yards, three yards. Even the natural body becomes a quantity when measured, as does the space which it occupies; but this is quantity accidental, not quantity essential; what we seek to grasp is not accidental quantity but Quantity independent and essential, Quantity-Absolute. Three oxen is not a quantity; it is their number, the three, that is Quantity; for in three oxen we are dealing with two categories. So too with a line of a stated length, a surface of a given area; the area will be a quantity but not the surface, which only comes under that category when it constitutes a definite geometric figure. #### Are we then to consider numbers, and numbers only, as constituting the category of Quantity? If we mean numbers in themselves, they are substances, for the very good reason that they exist independently. If we mean numbers displayed in the objects participant in number, the numbers which give the count of the objects- ten horses or ten oxen, and not ten units- then we have a paradoxical result: first, the numbers in themselves, it would appear, are substances but the numbers in objects are not; and secondly, the numbers inhere in the objects as measures [of extension or weight], yet as standing outside the objects they have no measuring power, as do rulers and scales. If however their existence is independent, and they do not inhere in the objects, but are simply called in for the purpose of measurement, the objects will be quantities only to the extent of participating in Quantity. #### So with the numbers themselves: how can they constitute the category of Quantity? They are measures; but how do measures come to be quantities or Quantity? Doubtless in that, existing as they do among the Existents and not being adapted to any of the other categories, they find their place under the influence of verbal suggestion and so are referred to the so-called category of Quantity. We see the unit mark off one measurement and then proceed to another; and number thus reveals the amount of a thing, and the mind measures by availing itself of the total figure. #### It follows that in measuring it is not measuring essence; it pronounces its "one" or "two," whatever the character of the objects, even summing contraries. It does not take count of condition- hot, handsome; it simply notes how many. #### Number then, whether regarded in itself or in the participant objects, belongs to the category of Quantity, but the participant objects do not. "Three yards long" does not fall under the category of Quantity, but only the three. #### Why then are magnitudes classed as quantities? Not because they are so in the strict sense, but because they approximate to Quantity, and because objects in which magnitudes inhere are themselves designated as quantities. We call a thing great or small from its participation in a high number or a low. True, greatness and smallness are not claimed to be quantities, but relations: but it is by their apparent possession of quantity that they are thought of as relations. All this, however, needs more careful examination. #### In sum, we hold that there is no single genus of Quantity. Only number is Quantity, the rest [magnitudes, space, time, motion] quantities only in a secondary degree. We have therefore not strictly one genus, but one category grouping the approximate with the primary and the secondary. #### We have however to enquire in what sense the abstract numbers are substances. Can it be that they are also in a manner quantitative? Into whatever category they fall, the other numbers [those inherent in objects] can have nothing in common with them but the name. ####  |